A generalized penalty function in Sparre Andersen risk models with surplus-dependent premium.

*(English)*Zbl 1229.91157The paper focuses on the surplus process of an insurance company, which is modeled as a generalized Sparre Andersen risk model with surplus-dependent premium rate. This assumption allows to obtain a twofold goal: maintaining a competitive level of premiums in case of higher surplus, as well as charging prudential higher premiums in case of insufficient funds.

Firstly, the generalized Gerber-Shiu function is derived by means of a transition function which is independent of the penalty function. Furthermore, properties of this last function are obtained under the assumption of a constant premium, or in the case of a threshold dividend strategy, or considering credit interest.

Some extensions are discussed within an absolute ruin model with debit interest.

Firstly, the generalized Gerber-Shiu function is derived by means of a transition function which is independent of the penalty function. Furthermore, properties of this last function are obtained under the assumption of a constant premium, or in the case of a threshold dividend strategy, or considering credit interest.

Some extensions are discussed within an absolute ruin model with debit interest.

Reviewer: Emilia Di Lorenzo (Napoli)

##### MSC:

91B30 | Risk theory, insurance (MSC2010) |

91B70 | Stochastic models in economics |

##### Keywords:

generalized penalty function; Gerber-Shiu function; Sparre Andersen model; surplus-dependent premium rate; dividend strategy; absolute ruin
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\textit{E. C. K. Cheung}, Insur. Math. Econ. 48, No. 3, 384--397 (2011; Zbl 1229.91157)

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